Elliott H. Lieb, Robert Seiringer
Proof of Bose-Einstein Condensation for Dilute Trapped Gases
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ABSTRACT.  The ground state of bosonic atoms in a trap has been shown 
experimentally to display Bose-Einstein condensation (BEC). We 
prove this fact theoretically for bosons with two-body repulsive 
interaction potentials in the dilute limit, starting from the basic 
Schroedinger equation; the condensation is 100% into the state 
that minimizes the Gross-Pitaevskii energy functional. This is 
the first rigorous proof of BEC in a physically realistic, 
continuum model.